10 beats/ are produced by the superposition of two sound waves. If the equation of the first wave is `y_(1) = 5 sin 20 pi (30t)`, then the equation of second wave is

Options

A. `y_(2) = 5 sin 20pi (31t)`
B. `y_(2) = 5 sin 20pi (30t)`
C. `y_(2) = 5 sin 20pi (32t)`
D. `y_(2) = 5 sin 21 pi (31t)`

Answer

A

Explanation

The equation `y_(1) = 5 sin 20pi (30t) = 5 sin (60pi t)`
Comparing this with the equation
`y = A sin omega t = A sin 2pi nt`, we get
`pi nt = 600 pit " " :. 2n = 600 or n = 300 Hz`
Since there are 10 beats/sec, the frequency of the other wave will be `300 -+ 10`Hz or 310 Hz or 290 Hz and the equation of the second wave will be either `y_(2) = 5 sin (620t) = 5 sin 20pi (31t)`..(1)
or `y_(2) = 5 sin (580t) = 5 sin 20pi (29t)`..(2)
`:.` From the given 4 equations, the correct choice is `y_(2) = 5 sin 20pi (31t)`...(a)